Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #22588628 | C2 | semidirect |
| 5. #22588625 | C2 | semidirect |
| 6. #22586460 | C2 | semidirect |
| 7. C71×#1391 | C2 | semidirect |
| 21. #17985793 | C4 | semidirect |
| 22. #17985791 | C4 | semidirect |
| 196. #1391 | D71 | semidirect |
| 197. C71 | #12969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597409 | 2 |
| #22590003 | 2 |
| #22588721 | 2 |
| #22588628 | 2 |
| #22588625 | 2 |
| #22586460 | 2 |
| C71×#1391 | 2 |
| #12969 | 71 |